Question: Solve for $x$ and $y$ using elimination. $\begin{align*}2x-9y &= 5 \\ -2x-5y &= 5\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-14y = 10$ Divide both sides by $-14$ and reduce as necessary. $y = -\dfrac{5}{7}$ Substitute $-\dfrac{5}{7}$ for $y$ in the top equation. $2x-9( -\dfrac{5}{7}) = 5$ $2x+\dfrac{45}{7} = 5$ $2x = -\dfrac{10}{7}$ $x = -\dfrac{5}{7}$ The solution is $\enspace x = -\dfrac{5}{7}, \enspace y = -\dfrac{5}{7}$.